Class 10 Exam > Class 10 Questions > The side of a square is 10 cm. What is the ar...
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The side of a square is 10 cm. What is the area of circumscribed circle?
- a)78.5 cm2
- b)157 cm2
- c)135 cm2
- d)314 cm2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The side of a square is 10 cm. What is the area of circumscribed circl...
Given:
Side of the square = 10 cm
To find:
The area of the circumscribed circle.
Solution:
To find the area of the circumscribed circle, we need to find the radius of the circle first.
Finding the radius:
The diagonal of a square divides it into two congruent right-angled triangles.
Let's consider one of these triangles.
In a right-angled triangle, the hypotenuse (diagonal of the square) is equal to the diameter of the circle and the length of one side of the square is equal to the radius of the circle.
Using the Pythagorean theorem, we can find the length of the diagonal of the square:
(diagonal)^2 = (side)^2 + (side)^2
(diagonal)^2 = 10^2 + 10^2
(diagonal)^2 = 100 + 100
(diagonal)^2 = 200
diagonal = √200 = 10√2 cm
Since the diagonal of the square is equal to the diameter of the circle, the diameter of the circle is 10√2 cm.
So, the radius of the circle = (10√2)/2 = 5√2 cm.
Finding the area of the circle:
The area of a circle is given by the formula: A = πr^2, where r is the radius of the circle.
Substituting the value of the radius, we get:
A = π(5√2)^2
A = π(25*2)
A = 50π cm^2
Now, let's approximate the value of π to 3.14.
A ≈ 50 * 3.14
A ≈ 157 cm^2
Therefore, the area of the circumscribed circle is approximately 157 cm^2.
Answer:
The correct answer is option b) 157 cm^2.
Side of the square = 10 cm
To find:
The area of the circumscribed circle.
Solution:
To find the area of the circumscribed circle, we need to find the radius of the circle first.
Finding the radius:
The diagonal of a square divides it into two congruent right-angled triangles.
Let's consider one of these triangles.
In a right-angled triangle, the hypotenuse (diagonal of the square) is equal to the diameter of the circle and the length of one side of the square is equal to the radius of the circle.
Using the Pythagorean theorem, we can find the length of the diagonal of the square:
(diagonal)^2 = (side)^2 + (side)^2
(diagonal)^2 = 10^2 + 10^2
(diagonal)^2 = 100 + 100
(diagonal)^2 = 200
diagonal = √200 = 10√2 cm
Since the diagonal of the square is equal to the diameter of the circle, the diameter of the circle is 10√2 cm.
So, the radius of the circle = (10√2)/2 = 5√2 cm.
Finding the area of the circle:
The area of a circle is given by the formula: A = πr^2, where r is the radius of the circle.
Substituting the value of the radius, we get:
A = π(5√2)^2
A = π(25*2)
A = 50π cm^2
Now, let's approximate the value of π to 3.14.
A ≈ 50 * 3.14
A ≈ 157 cm^2
Therefore, the area of the circumscribed circle is approximately 157 cm^2.
Answer:
The correct answer is option b) 157 cm^2.
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Community Answer
The side of a square is 10 cm. What is the area of circumscribed circl...
Diameter of the circumscribed circle
= diagonal of the square
= 10√2cm
Radius =
= diagonal of the square
= 10√2cm
Radius =
Area of circumscribed circle = πr2
= 157 cm2.
= 157 cm2.
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The side of a square is 10 cm. What is the area of circumscribed circle?a)78.5 cm2b)157 cm2c)135 cm2d)314 cm2Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The side of a square is 10 cm. What is the area of circumscribed circle?a)78.5 cm2b)157 cm2c)135 cm2d)314 cm2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The side of a square is 10 cm. What is the area of circumscribed circle?a)78.5 cm2b)157 cm2c)135 cm2d)314 cm2Correct answer is option 'B'. Can you explain this answer?.
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